Poisson Algebra of Diffeomorphism Generators in a Spacetime Containing a Bifurcation
نویسنده
چکیده
In this article we will analyze the possibility of a nontrivial central extension of the Poisson algebra of the diffeomorphisms generators which respect certain boundary conditions on the black hole bifurcation. The origin of a possible central extension in the algebra is due to the existence of boundary terms in the canonical generators, which are necessary to make them differentiable. The existence of such boundary terms depends on the exact boundary conditions that one takes. We will check two possible boundary conditions on the black hole bifurcation: Fixed metric and fixed surface gravity. In the case of fixed metric of the bifurcation the action acquires a boundary term but this term is canceled in the Legendre transformation and so absent in the Hamiltonian, and so in this case the possibility of a central extension is ruled out. In the case of fixed surface gravity the boundary term in the action is absent but therefore present in the Hamiltonian. Also in this case case we will see that there is no central extension, also if there exist boundary terms in the generators. ∗e-mail: [email protected]
منابع مشابه
Canonical Gravity, Diffeomorphisms and Objective Histories
This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the diffeomorphism invariance of the Lagrangian results in the following properties of the constrained Hamiltonian theory: the diffeomorphisms are generated by cons...
متن کاملGauge Symmetries of the N=2 String
We study the underlying gauge symmetry algebra of the N = 2 string, which is broken down to a subalgebra in any spacetime background. For given toroidal backgrounds, the unbroken gauge symmetries (corresponding to holomorphic and antiholomorphic worldsheet currents) generate area-preserving diffeomorphism algebras of null 2-tori. A minimal Lie algebraic closure containing all the gauge symmetri...
متن کاملκ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl–Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained...
متن کاملCauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping
متن کامل
General Two-Dimensional Supergravity from Poisson Superalgebras
We provide the geometric actions for most general N = 1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N . This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an (essentially) arbitrary function of curvature and torsion. Technically we proceed as follows: The bosonic part of any of thes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004